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Re: Summation problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg56675] Re: [mg56621] Summation problem
*From*: Devendra Kapadia <dkapadia at wolfram.com>
*Date*: Tue, 3 May 2005 05:26:26 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
On Sat, 30 Apr 2005, jaropis wrote:
> Why can't Mathematica sum:
> Sum[I^n/n,{n,1,Infinity}]
> and gives the (incorrect) answer, that this is divergent while it can do:
> Sum[I^(n+1)/n,{n,1,Infinity}]
> correctly?
>
> Jaroslaw Piskorski
>
Hello Jaroslaw Piskorski,
Thank you for reporting this problem with an infinite sum.
This is caused by a failure to detect the conditional convergence
of the sum in your first example, in Mathematica 5.
A workaround for the problem is to replace 'I' by the symbolic
quantity 'x' and then substitute 'x' with 'I', as shown below.
==========================================================
In[1]:= $Version
Out[1]= 5.1 for Linux (February 20, 2005)
In[2]:= Sum[x^n/n,{n,1,Infinity}]/.{x-> I}
Out[2]= -Log[1 - I]
In[3]:= N[%]
Out[3]= -0.346574 + 0.785398 I
In[4]:= NSum[I^n/n,{n,1,Infinity}]
Out[4]= -0.346574 + 0.785398 I
============================================================
Sorry for the inconvenience caused by this problem.
Devendra Kapadia.
Wolfram Research, Inc.
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